This paper addresses the problem of predicting machine failures in an industrial manufacturing process based on multivariate time series data. A workflow is presented for cleaning and preprocessing the data, and for training and evaluating a predictive model. Its implementation is modular and extensible to support changes in the underlying production processes and the gathered data. Two predictive models are presented, based on Convolutional Neural Networks and Recurrent Neural Networks, and evaluated on data from an advanced machining process used for cutting complex shapes into metal pieces.